Problem: Solve for $x$ and $y$ using elimination. ${-x+2y = 6}$ ${x+5y = 29}$
Explanation: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $-x$ and $x$ cancel out. $7y = 35$ $\dfrac{7y}{{7}} = \dfrac{35}{{7}}$ ${y = 5}$ Now that you know ${y = 5}$ , plug it back into $\thinspace {-x+2y = 6}\thinspace$ to find $x$ ${-x + 2}{(5)}{= 6}$ $-x+10 = 6$ $-x+10{-10} = 6{-10}$ $-x = -4$ $\dfrac{-x}{{-1}} = \dfrac{-4}{{-1}}$ ${x = 4}$ You can also plug ${y = 5}$ into $\thinspace {x+5y = 29}\thinspace$ and get the same answer for $x$ : ${x + 5}{(5)}{= 29}$ ${x = 4}$